Scoring documents in a linked database

ABSTRACT

A method assigns importance ranks to nodes in a linked database, such as any database of documents containing citations, the world wide web or any other hypermedia database. The rank assigned to a document is calculated from the ranks of documents citing it. In addition, the rank of a document is calculated from a constant representing the probability that a browser through the database will randomly jump to the document. The method is particularly useful in enhancing the performance of search engine results for hypermedia databases, such as the world wide web, whose documents have a large variation in quality.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/209,687, filed Aug. 24, 2005, now abandoned, which is a continuationof U.S. patent application Ser. No. 09/895,174, filed Jul. 2, 2001, nowU.S. Pat. No. 7,058,628, which is a continuation of U.S. patentapplication Ser. No. 09/004,827, filed Jan. 9, 1998, now U.S. Pat. No.6,285,999, which claims priority from U.S. provisional patentapplication No. 60/035,205 filed Jan. 10, 1997, which are allincorporated herein by reference.

STATEMENT REGARDING GOVERNMENT SUPPORT

This invention was supported in part by the National Science Foundationgrant number IRI-9411306-4. The Government has certain rights in theinvention.

FIELD OF THE INVENTION

This invention relates generally to techniques for analyzing linkeddatabases. More particularly, it relates to methods for assigning ranksto nodes in a linked database, such as any database of documentscontaining citations, the world wide web or any other hypermediadatabase.

BACKGROUND OF THE INVENTION

Due to the developments in computer technology and its increase inpopularity, large numbers of people have recently started to frequentlysearch huge databases. For example, internet search engines arefrequently used to search the entire world wide web. Currently, apopular search engine might execute over 30 million searches per day ofthe indexable part of the web, which has a size in excess of 500Gigabytes. Information retrieval systems are traditionally judged bytheir precision and recall. What is often neglected, however, is thequality of the results produced by these search engines. Large databasesof documents such as the web contain many low quality documents. As aresult, searches typically return hundreds of irrelevant or unwanteddocuments which camouflage the few relevant ones. In order to improvethe selectivity of the results, common techniques allow the user toconstrain the scope of the search to a specified subset of the database,or to provide additional search terms. These techniques are mosteffective in cases where the database is homogeneous and alreadyclassified into subsets, or in cases where the user is searching forwell known and specific information. In other cases, however, thesetechniques are often not effective because each constraint introduced bythe user increases the chances that the desired information will beinadvertently eliminated from the search results.

Search engines presently use various techniques that attempt to presentmore relevant documents. Typically, documents are ranked according tovariations of a standard vector space model. These variations couldinclude (a) how recently the document was updated, and/or (b) how closethe search terms are to the beginning of the document. Although thisstrategy provides search results that are better than with no ranking atall, the results still have relatively low quality. Moreover, whensearching the highly competitive web, this measure of relevancy isvulnerable to “spamming” techniques that authors can use to artificiallyinflate their document's relevance in order to draw attention to it orits advertisements. For this reason search results often containcommercial appeals that should not be considered a match to the query.Although search engines are designed to avoid such ruses, poorlyconceived mechanisms can result in disappointing failures to retrievedesired information.

Hyperlink Search Engine, developed by IDD Information Services,(http://rankdex.gari.com/) uses backlink information (i.e., informationfrom pages that contain links to the current page) to assist inidentifying relevant web documents. Rather than using the content of adocument to determine relevance, the technique uses the anchor text oflinks to the document to characterize the relevance of a document. Theidea of associating anchor text with the page the text points to wasfirst implemented in the World Wide Web Worm (Oliver A. McBryan, GENVLand WWWW: Tools for Taming the Web, First International Conference onthe World Wide Web, CERN, Geneva, May 25-27, 1994). The Hyperlink SearchEngine has applied this idea to assist in determining document relevancein a search. In particular, search query terms are compared to acollection of anchor text descriptions that point to the page, ratherthan to a keyword index of the page content. A rank is then assigned toa document based on the degree to which the search terms match theanchor descriptions in its backlink documents.

The well known idea of citation counting is a simple method fordetermining the importance of a document by counting its number ofcitations, or backlinks. The citation rank r(A) of a document which hasn backlink pages is simplyr(A)=n.

In the case of databases whose content is of relatively uniform qualityand importance it is valid to assume that a highly cited document shouldbe of greater interest than a document with only one or two citations.Many databases, however, have extreme variations in the quality andimportance of documents. In these cases, citation ranking is overlysimplistic. For example, citation ranking will give the same rank to adocument that is cited once on an obscure page as to a similar documentthat is cited once on a well-known and highly respected page.

SUMMARY

Various aspects of the present invention provide systems and methods forranking documents in a linked database. One aspect provides an objectiveranking based on the relationship between documents. Another aspect ofthe invention is directed to a technique for ranking documents within adatabase whose content has a large variation in quality and importance.Another aspect of the present invention is to provide a document rankingmethod that is scalable and can be applied to extremely large databasessuch as the world wide web. Additional aspects of the invention willbecome apparent in view of the following description and associatedfigures.

The present invention achieves the above objects by taking advantage ofthe linked structure of a database to assign a rank to each document inthe database, where the document rank is a measure of the importance ofa document. Rather than determining relevance from the intrinsic contentof a document, or from the anchor text of backlinks to the document, thepresent method determines importance from the extrinsic relationshipsbetween documents. Intuitively, a document should be important(regardless of its content) if it is highly cited by other documents.Not all citations, however, are of equal significance. A citation froman important document is more important than a citation from arelatively unimportant document. Thus, the importance of a page, andhence the rank assigned to it, should depend not just on the number ofcitations it has, but on the importance of the citing documents as well.This implies a recursive definition of rank: the rank of a document is afunction of the ranks of the documents which cite it. The ranks ofdocuments may be calculated by an iterative procedure on a linkeddatabase.

Because citations, or links, are ways of directing attention, theimportant documents correspond to those documents to which the mostattention is directed. Thus, a high rank indicates that a document isconsidered valuable by many people or by important people. Most likely,these are the pages to which someone performing a search would like todirect his or her attention. Looked at another way, the importance of apage is directly related to the steady-state probability that a randomweb surfer ends up at the page after following a large number of links.Because there is a larger probability that a surfer will end up at animportant page than at an unimportant page, this method of ranking pagesassigns higher ranks to the more important pages.

In one aspect of the invention, a computer implemented method isprovided for calculating an importance rank for N linked nodes of alinked database. The method comprises the steps of:

(a) selecting an initial N-dimensional vector p₀;

(b) computing an approximation p_(n) to a steady-state probability p_(∞)in accordance with the equation p_(n)=A^(n)p₀, where A is an N×Ntransition probability matrix having elements A[i][j] representing aprobability of moving from node i to node j; and

(c) determining a rank r[k] for a node k from a k^(th) component ofp_(n).

In a preferred embodiment, the matrix A is chosen so that an importancerank of a node is calculated, in part, from a weighted sum of importanceranks of backlink nodes of the node, where each of the backlink nodes isweighted in dependence upon the total number of links in the backlinknode. In addition, the importance rank of a node is calculated, in part,from a constant α representing the probability that a surfer willrandomly jump to the node. The importance rank of a node can also becalculated, in part, from a measure of distances between the node andbacklink nodes of the node. The initial N-dimensional vector p₀ may beselected to represent a uniform probability distribution, or anon-uniform probability distribution which gives weight to apredetermined set of nodes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of the relationship between three linked hypertextdocuments according to the invention.

FIG. 2 is a diagram of a three-document web illustrating the rankassociated with each document in accordance with the present invention.

FIG. 3 is a flowchart of one implementation of the invention.

DETAILED DESCRIPTION

Although the following detailed description contains many specifics forthe purposes of illustration, anyone of ordinary skill in the art willappreciate that many variations and alterations to the following detailsare within the scope of the invention. Accordingly, the followingembodiments of the invention are set forth without any loss ofgenerality to, and without imposing limitations upon, the claimedinvention. For support in reducing the present invention to practice,the inventor acknowledges Sergey Brin, Scott Hassan, Rajeev Motwani,Alan Steremberg, and Terry Winograd.

A linked database (i.e. any database of documents containing mutualcitations, such as the world wide web or other hypermedia archive, adictionary or thesaurus, and a database of academic articles, patents,or court cases) can be represented as a directed graph of N nodes, whereeach node corresponds to a web page document and where the directedconnections between nodes correspond to links from one document toanother. A given node has a set of forward links that connect it tochildren nodes, and a set of backward links that connect it to parentnodes. FIG. 1 shows a typical relationship between three hypertextdocuments A, B, and C. As shown in this particular figure, the firstlinks in documents B and C are pointers to document A. In this case wesay that B and C are backlinks of A, and that A is a forward link of Band of C. Documents B and C also have other forward links to documentsthat are not shown.

Although the ranking method of the present invention is superficiallysimilar to the well known idea of citation counting, the present methodis more subtle and complex than citation counting and gives far superiorresults. In a simple citation ranking, the rank of a document A whichhas n backlink pages is simplyr(A)=n.

According to one embodiment of the present method of ranking, thebacklinks from different pages are weighted differently and the numberof links on each page is normalized. More precisely, the rank of a pageA is defined according to the present invention as

${{r(A)} = {\frac{\alpha}{N} + {\left( {1 - \alpha} \right)\left( {\frac{r\left( B_{1} \right)}{B_{1}} + \ldots + \frac{r\left( B_{n} \right)}{B_{n}}} \right)}}},$where B₁, . . . , B_(n) are the backlink pages of A, r(B₁), . . . ,r(B_(n)) are their ranks, |B₁|, . . . , |B_(n)| are their numbers offorward links, and α is a constant in the interval [0,1], and N is thetotal number of pages in the web. This definition is clearly morecomplicated and subtle than the simple citation rank. Like the citationrank, this definition yields a page rank that increases as the number ofbacklinks increases. But the present method considers a citation from ahighly ranked backlink as more important than a citation from a lowlyranked backlink (provided both citations come from backlink documentsthat have an equal number of forward links). In the present invention,it is possible, therefore, for a document with only one backlink (from avery highly ranked page) to have a higher rank than another documentwith many backlinks (from very low ranked pages). This is not the casewith simple citation ranking.

The ranks form a probability distribution over web pages, so that thesum of ranks over all web pages is unity. The rank of a page can beinterpreted as the probability that a surfer will be at the page afterfollowing a large number of forward links. The constant α in the formulais interpreted as the probability that the web surfer will jump randomlyto any web page instead of following a forward link. The page ranks forall the pages can be calculated using a simple iterative algorithm, andcorresponds to the principal eigenvector of the normalized link matrixof the web, as will be discussed in more detail below.

In order to illustrate the present method of ranking, consider thesimple web of three documents shown in FIG. 2. For simplicity ofillustration, we assume in this example that r=0. Document A has asingle backlink to document C, and this is the only forward link ofdocument C, sor(A)=r(C).

Document B has a single backlink to document A, but this is one of twoforward links of document A, sor(B)=r(A)/2.

Document C has two backlinks. One backlink is to document B, and this isthe only forward link of document B. The other backlink is to document Avia the other of the two forward links from A. Thusr(C)=r(B)+r(A)/2.

In this simple illustrative case we can see by inspection that r(A)=0.4,r(B)=0.2, and r(C)=0.4. Although a typical value for α is ˜0.1, if forsimplicity we set α=0.5 (which corresponds to a 50% chance that a surferwill randomly jump to one of the three pages rather than following aforward link), then the mathematical relationships between the ranksbecome more complicated. In particular, we then haver(A)=1/6+r(C)/2,r(B)=1/6+r(A)/4, andr(C)=1/6+r(A)/4+r(B)/2.

The solution in this case is r(A)=14/39, r(B)=10/39, and r(C)=15/39.

In practice, there are millions of documents and it is not possible tofind the solution to a million equations by inspection. Accordingly, inthe preferred embodiment a simple iterative procedure is used. As theinitial state we may simply set all the ranks equal to 1/N. The formulasare then used to calculate a new set of ranks based on the existingranks. In the case of millions of documents, sufficient convergencetypically takes on the order of 100 iterations. It is not alwaysnecessary or even desirable, however, to calculate the rank of everypage with high precision. Even approximate rank values, using two ormore iterations, can provide very valuable, or even superior,information.

The iteration process can be understood as a steady-state probabilitydistribution calculated from a model of a random surfer. This model ismathematically equivalent to the explanation described above, butprovides a more direct and concise characterization of the procedure.The model includes (a) an initial N-dimensional probability distributionvector p₀ where each component p₀[i] gives the initial probability thata random surfer will start at a node i, and (b) an N×N transitionprobability matrix A where each component A[i][j] gives the probabilitythat the surfer will move from node i to node j. The probabilitydistribution—of the graph after the surfer follows one link is p₁=Ap₀,and after two links the probability distribution is p₂=Ap₁=A²p₀.Assuming this iteration converges, it will converge to a steady-stateprobability

$p_{\infty} = {\lim\limits_{n\rightarrow\infty}{A^{n}p_{0}}}$which is a dominant eigenvector of A. The iteration circulates theprobability through the linked nodes like energy flows through a circuitand accumulates in important places. Because pages with no links occurin significant numbers and bleed off energy, they cause somecomplication with computing the ranking. This complication is caused bythe fact they can add huge amounts to the “random jump” factor. This, inturn, causes loops in the graph to be highly emphasized which is notgenerally a desirable property of the model. In order to address thisproblem, these childless pages can simply be removed from the modelduring the iterative stages, and added back in after the iteration iscomplete. After the childless pages are added back in, however, the samenumber of iterations that was required to remove them should be done tomake sure they all receive a value. (Note that in order to ensureconvergence, the norm of p_(i) must be made equal to 1 after eachiteration.) An alternate method to control the contribution of thechildless nodes is to only estimate the steady state by iterating asmall number of times.

The rank r[i] of a node i can then be defined as a function of thissteady-state probability distribution. For example, the rank can bedefined simply by r[i]=p_(∞)[i]. This method of calculating rank ismathematically equivalent to the iterative method described first. Thoseskilled in the art will appreciate that this same method can becharacterized in various different ways that are mathematicallyequivalent. Such characterizations are obviously within the scope of thepresent invention. Because the rank of various different documents canvary by orders of magnitude, it is convenient to define a logarithmicrank

${r\lbrack i\rbrack} = {\log\frac{p_{\infty}\lbrack i\rbrack}{\min\limits_{k \in {\lbrack{1,N}\rbrack}}\left\{ {p_{\infty}\lbrack k\rbrack} \right\}}}$which assigns a rank of 0 to the lowest ranked node and increases by 1for each order of magnitude in importance higher than the lowest rankednode.

FIG. 3 shows one embodiment of a computer implemented method forcalculating an importance rank for N linked nodes of a linked database.At a step 101, an initial N-dimensional vector p₀ is selected. Anapproximation p_(n), to a steady-state probability p_(∞) in accordancewith the equation p_(n)=A^(n)p₀ is computed at a step 103. Matrix A canbe an N×N transition probability matrix having elements A[i][j]representing a probability of moving from node i to node j. At a step105, a rank r[k] for node k from a k^(th) component of p_(n) isdetermined.

In one particular embodiment, a finite number of iterations areperformed to approximate p_(∞). The initial distribution can be selectedto be uniform or non-uniform. A uniform distribution would set eachcomponent of p₀ equal to 1/N. A non-uniform distribution, for example,can divide the initial probability among a few nodes which are known apriori to have relatively large importance. This non-uniformdistribution decreases the number of iterations required to obtain aclose approximation to p_(∞) and also is one way to reduce the effect ofartificially inflating relevance by adding unrelated terms.

In another particular embodiment, the transition matrix A is given by

${A = {{\frac{\alpha}{N}11} + {\left( {1 - \alpha} \right)B}}},$where 11 is an N×N matrix consisting of all 1s, α is the probabilitythat a surfer will jump randomly to any one of the N nodes, and B is amatrix whose elements B[i][j] are given by

${{B\lbrack i\rbrack}\lbrack j\rbrack} = \left\{ {\begin{matrix}\frac{1}{n_{i}} & {{if}\mspace{14mu}{node}\mspace{14mu} i\mspace{14mu}{points}\mspace{14mu}{to}\mspace{14mu}{node}\mspace{14mu} j} \\0 & {otherwise}\end{matrix},} \right.$where n_(i) is the total number of forward links from node i. The (1−α)factor acts as a damping factor that limits the extent to which adocument's rank can be inherited by children documents. This models thefact that users typically jump to a different place in the web afterfollowing a few links. The value of α is typically around 15%. Includingthis damping is important when many iterations are used to calculate therank so that there is no artificial concentration of rank importancewithin loops of the web. Alternatively, one may set α=0 and only iteratea few times in the calculation.

Consistent with the present invention, there are several ways that thismethod can be adapted or altered for various purposes. As alreadymentioned above, rather than including the random linking probability αequally among all nodes, it can be divided in various ways among all thesites by changing the 11 matrix to another matrix. For example, it couldbe distributed so that a random jump takes the surfer to one of a fewnodes that have a high importance, and will not take the surfer to anyof the other nodes. This can be very effective in preventing deceptivelytagged documents from receiving artificially inflated relevance.Alternatively, the random linking probability could be distributed sothat random jumps do not happen from high importance nodes, and onlyhappen from other nodes. This distribution would model a surfer who ismore likely to make random jumps from unimportant sites and followforward links from important sites. A modification to avoid drawingunwarranted attention to pages with artificially inflated relevance isto ignore local links between documents and only consider links betweenseparate domains. Because the links from other sites to the document arenot directly under the control of a typical web site designer, it isthen difficult for the designer to artificially inflate the ranking. Asimpler approach is to weight links from pages contained on the same webserver less than links from other servers. Also, in addition to servers,internet domains and any general measure of the distance between linkscould be used to determine such a weighting.

Additional modifications can further improve the performance of thismethod. Rank can be increased for documents whose backlinks aremaintained by different institutions and authors in various geographiclocations. Or it can be increased if links come from unusually importantweb locations such as the root page of a domain.

Links can also be weighted by their relative importance within adocument. For example, highly visible links that are near the top of adocument can be given more weight. Also, links that are in large fontsor emphasized in other ways can be given more weight. In this way, themodel better approximates human usage and authors' intentions. In manycases it is appropriate to assign higher value to links coming frompages that have been modified recently since such information is lesslikely to be obsolete.

Various implementations of the invention have the advantage that theconvergence is very fast (a few hours using current processors) and itis much less expensive than building a full-text index. This speedallows the ranking to be customized or personalized for specific users.For example, a user's home page and/or bookmarks can be given a largeinitial importance, and/or a high probability of a random jump returningto it. This high rating essentially indicates to the system that theperson's homepage and/or bookmarks does indeed contain subjects ofimportance that should be highly ranked. This procedure essentiallytrains the system to recognize pages related to the person's interests.

The present method of determining the rank of a document can also beused to enhance the display of documents. In particular, each link in adocument can be annotated with an icon, text, or other indicator of therank of the document that each link points to. Anyone viewing thedocument can then easily see the relative importance of various links inthe document.

The present method of ranking documents in a database can also be usefulfor estimating the amount of attention any document receives on the websince it models human behavior when surfing the web. Estimating theimportance of each backlink to a page can be useful for many purposesincluding site design, business arrangements with the backlinkers, andmarketing. The effect of potential changes to the hypertext structurecan be evaluated by adding them to the link structure and recomputingthe ranking.

Real usage data, when available, can be used as a starting point for themodel and as the distribution for the alpha factor. This can allow thisranking model to fill holes in the usage data, and provide a moreaccurate or comprehensive picture. Thus, although this method of rankingdoes not necessarily match the actual traffic, it nevertheless measuresthe degree of exposure a document has throughout the web.

Another application and embodiment of the present invention is directedto enhancing the quality of results from web search engines. In thisapplication of the present invention, a ranking method according to theinvention is integrated into a web search engine to produce results farsuperior to existing methods in quality and performance. A search engineemploying a ranking method of the present invention provides automationwhile producing results comparable to a human maintained categorizedsystem. In this approach, a web crawler explores the web and creates anindex of the web content, as well as a directed graph of nodescorresponding to the structure of hyperlinks. The nodes of the graph(i.e., pages of the web) are then ranked according to importance asdescribed above in connection with various exemplary embodiments of thepresent invention.

The search engine is used to locate documents that match the specifiedsearch criteria, either by searching full text, or by searching titlesonly. In addition, the search can include the anchor text associatedwith backlinks to the page. This approach has several advantages in thiscontext. First, anchors often provide more accurate descriptions of webpages than the pages themselves. Second, anchors may exist for images,programs, and other objects that cannot be indexed by a text-basedsearch engine. This also makes it possible to return web pages whichhave not actually been crawled. In addition, the engine can compare thesearch terms with a list of its backlink document titles. Thus, eventhough the text of the document itself may not match the search terms,if the document is cited by documents whose titles or backlink anchortext match the search terms, the document will be considered a match. Inaddition to or instead of the anchor text, the text in the immediatevicinity of the backlink anchor text can also be compared to the searchterms in order to improve the search.

Once a set of documents is identified that match the search terms, thelist of documents is then sorted with high ranking documents first andlow ranking documents last. The ranking in this case is a function whichcombines all of the above factors such as the objective ranking andtextual matching. If desired, the results can be grouped by category orsite as well.

It will be clear to one skilled in the art that the above embodimentsmay be altered in many ways without departing from the scope of theinvention. Accordingly, the scope of the invention should be determinedby the following claims and their legal equivalents.

1. A method performed by a computer, the method comprising: identifying,by the computer, links from linking documents to linked documents in anetwork; determining, by the computer, a measure of importance of theidentified links; assigning, by the computer, a weight value to each ofthe identified links based on the determined measure of importance ofthe identified link; assigning, by the computer, a score to one of thelinked documents based on the weight value assigned to one or more ofthe identified links that point to the one of the linked documents; andstoring, by the computer, the score for the one of the linked documents.2. The method of claim 1, where the measure of importance, of each ofthe identified links, is based on a measure of quality associated withthe corresponding linking document.
 3. The method of claim 1, where thelinking documents and the linked documents comprise at least a milliondocuments on the world wide web.
 4. The method of claim 1, where themeasure of importance, of each of the identified links, is based onwhether the corresponding linking document is stored on a same server asthe linked document.
 5. The method of claim 1, where the measure ofimportance, of each of the identified links, is based on a measure ofimportance of a location at which the corresponding linking document isstored.
 6. The method of claim 1, where the measure of importance, ofeach of the identified links, is based on a position of the identifiedlink within the corresponding linking document.
 7. The method of claim1, where the measure of importance, of each of the identified links, isbased on a visibility of the identified link within the correspondinglinking document relative to a visibility of another link within thecorresponding linking document.
 8. The method of claim 7, where thevisibility, of the identified link within the corresponding linkingdocument, is associated with a font size of text associated with theidentified link.
 9. The method of claim 1, where the measure ofimportance, of each of the identified links, is based on a date on whichthe corresponding linking document was last modified.
 10. The method ofclaim 1, where the measure of importance, of each of the identifiedlinks, is based on user behavior with regard to a parameter associatedwith the identified link within the corresponding linking document. 11.A method performed by a computer, the method comprising: identifyingdocuments in a network; scoring the identified documents based on scoresof documents pointing to the identified documents and a damping factorused to avoid loops when scoring the identified documents; and storingscores for the identified documents.
 12. The method of claim 11, wherethe documents include at least a million documents on the world wideweb.
 13. A method performed by a computer, the method comprising:identifying, by the computer, documents in a network; scoring, by thecomputer, the identified documents based on scores of documents pointingto the identified documents and a component representing a random jumpbetween documents in the network; and storing, by the computer, scoresfor the identified documents.
 14. The method of claim 13, where thedocuments include at least a million documents on the world wide web.15. A method performed by a computer, the method comprising:identifying, by the computer, at least a million documents on the worldwide web; generating, by the computer, scores for the identifieddocuments, the score, for one of the identified documents, being basedon a respective score of each of a plurality of the identified documentsthat includes a link to the one of the identified documents and arespective quality of links originating from each of the plurality ofthe identified documents; and storing, by the computer, the scores forthe identified documents.
 16. The method of claim 15, where the score,for the one of the identified documents, is further based on a totalquantity of the identified documents.
 17. The method of claim 15, wherethe score, for the one of the identified documents, is based onrespective values corresponding to the plurality of the identifieddocuments, the respective value, corresponding to one of the pluralityof the identified documents, including the respective score associatedwith the one of the plurality of the identified documents divided by therespective quantity of links originating from the one of the pluralityof the identified documents.
 18. The method of claim 15, where thescore, for the one of the identified documents, is based on a summationof respective values corresponding to the plurality of the identifieddocuments, the respective value, corresponding to one of the pluralityof the identified documents, including the respective score associatedwith the one of the plurality of the identified documents divided by therespective quantity of links originating from the one of the pluralityof the identified documents.
 19. The method of claim 15, where thescore, for the one of the identified documents, is further based on avalue that reflects a probability that a surfer will randomly jump toany one of the identified documents rather than selecting a link from aparticular one of the identified documents.
 20. The method of claim 19,where the probability, for the one of the identified documents, differsfrom a probability for another one of the identified documents.